There are two types of air flow problems that can cause overheating. One of them was mentioned by Denman: obstruction. (Typically by lint buildup obstructing the lint trap or exhaust ducts or exhaust vent. Possibly by lint blocking the air intake holes at the back of the drum. Possibly by something covering the air intake vent at the back of the dryer.)
The other type of air flow problem is a leaking seal. A leaky seal creates an undesirable alternate path that allows a portion of the heated air to flow OUTSIDE the drum. The heated air that flows outside the drum will heat up the dryer cabinet and may blow the thermal fuse.
So I recommend you inspect the seal(s). According to the list of parts for the Kenmore dryer, the seal is a circular strip of felt at the front of the drum, where the front of the drum mates with the inside of the dryer's front panel.
Your dryer may also have a seal at the back, but my intuition is that a leak at the back is less of a problem than a leak at the front since a leak at the back involves only a minimal length air path outside the drum. If the seal at the front is okay, check the seal at the back.
There may be an additional seal lining the dryer door, which is easy to examine. I think the door seal is less likely to undergo significant wear and tear than the seals around which the drum rotates, but if it's bad it would allow air to be sucked in at the door, which would reduce the amount of hot air sucked into the back of the drum, which could cause the hot air at the back to overheat the dryer cabinet.
By the way, my observations of temperatures inside my dryer taught me that neither the control thermostat (which senses the exhaust temperature) nor the dryer's temperature control dial (high heat, medium heat, low heat) are designed to have any effect except near the end of the cycle, when little moisture remains in the clothes. Until then, evaporating moisture causes the clothes and the exhaust to remain relatively cool. (If you don't understand this, try googling "evaporative cooling.") So, for most of the drying cycle, the cool exhaust causes the control thermostat to stay closed, which causes the heating coil to stay fully on (even when the dial is set to low heat) until the clothes are nearly dry. (This applies only to the high heat, medium heat and low heat settings, not to the "no heat" setting, of course.) The heating coil is designed to always be either fully on or fully off; the low heat setting causes the heat to turn off more frequently than the medium or high settings, but only when little moisture remains in the clothes, which is when heat-sensitive clothes might get too hot.
That means the control thermostat and the temperature control dial are irrelevant to a thermal fuse blowing problem. If your heat-sensitive clothes get damaged when the dryer is set to low heat, that's a situation in which the control thermostat or control dial may be relevant. (If the dryer heats when the dryer is set to "no heat" that's another situation when the control dial--but not the control thermostat--may be relevant.)
I guess I disagree with some of what Denman suggested you check. Your dryer is overheating long before the clothes are nearly dry. I think the dryer shouldn't overheat even if thermostats or relays are stuck closed, because during normal operation the heating coil is designed to be fully on anyway (until the clothes are nearly dry). For the same reason, the exhaust temperature is irrelevant since it should be too cool to open the control thermostat until the clothes are nearly dry. And changing from high heat to low heat won't affect the heat or the exhaust temperature until the clothes are nearly dry. (If I'm mistaken about any of these things, I hope Denman will explain why.) I agree with Denman that air obstruction is the first thing to check since it's the most typical cause. And I agree that a partially shorted heating coil might be the problem, since the full voltage would travel through less resistance, causing greater current than designed, and the heat produced by a resistor is proportional to the product of voltage and current.
If you want to monitor temperature, the Uni-T UT200 multimeter sells for about $15 at Amazon. (I bought one recently, so now I have two multimeters and can observe two temperatures simultaneously. Observing temperatures at both fuse and high limit thermostat helped my understanding of my dryer's operation.) If you don't already have a multimeter with a temperature probe, it might pay for itself quickly by letting you protect your dryer's fuse until you've fixed the overheating problem; you could switch the dryer's temperature control dial to "no heat" each time the temperature at the fuse approaches the fuse's blowing temperature.
